Ballistic comparison tests rely on the striations and impressions that are created on the surface of a ballistic piece of evidence (BPOE) such as a bullet or cartridge case. These striations have unique features that represent a unique signature of a firearm. By comparing the striations or impressed characteristics of two BPOE, it may be possible to conclude if they have been fired from the same firearm.
When acquiring 3D topography images of an area on an object, i.e. a relief map Z(x, y) where Z is the local height of the surface at position (x, y), an optical system including a sensor (or camera) and a light source is used. An object under study is illuminated and a topographic image of the illuminated surface is acquired.
In the field of ballistics, objects under study are often non-planar and likely specular. This means that most of the incident light from an angle θ with respect to the local surface normal N will be reflected in a small cone pointing in the direction −θ. Therefore, if the light source is placed along the optical axis of the sensor, as it is the case for numerous optical methods for topography capture, only an infinitesimal part of incident light is reflected back into the sensor for portions of the topography showing significant slopes, leading to locally invalid measurements.
A totally different method of measuring the topography of an object exists. According to the method, known as photometric stereo, a set of radiance (or energetic luminance) images of the surface are acquired, with different lighting conditions for each image of the set. If a constant reflectivity of the surface and identical illumination strength of the light sources are assumed and if the surface is purely diffusive (or Lambertian), three light sources are sufficient to retrieve the surface normal field N(x,y). The topography Z(x,y) of the surface is obtained through integration of the normal field.
However, radiance images of a surface are subjected to noise and the surface reflectivity might not be constant due to local variation of color and/or albedo. A common solution is to use a greater number of light sources in order to over define the linear system of equations. The surface normal field N(x,y) is then obtained though an error minimization procedure such as the chi square error minimization scheme. If the number of light sources is large enough, one can even afford not to measure the intensity of the light sources, or even the light source positions, and obtain this information through a fitting procedure, Principal Component analysis, or other methods known to those skilled in the art.
Very few surfaces are truly diffusive and applying the aforementioned procedure leads to very poor results in terms of accuracy of the topography if the surface is glossy or shiny. However, when the viewing direction is far from the specular reflection direction for a particular light source, the Lambert model of light reflection on a surface might still hold to a certain extent. Again, the common solution when facing such a shiny or glossy material is to over define the problem by using more than three light sources and determine, for every pixel of the resulting image set, if any light source produces a reflection toward the camera that is dominated by non Lambertian contribution. If such a condition is found, the contribution of this light source is ignored in the computation of the surface normal N of the considered pixel.
However, when considering ballistic pieces of evidence (BPOE), none of these methods work since the surface is metallic, which leads to a diffusive contribution of light reflection, if any, that is orders of magnitude lower than the specular contribution. There is therefore a need to improve photometric stereo for the capture of metallic surfaces in general and for BPOE's in particular.